Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}6x-3y &= 9 \\ -6x+2y &= -7\end{align*}$
Begin by moving the $x$ -term in the second equation to the right side of the equation. $2y = 6x-7$ Divide both sides by $2$ to isolate $y$ $y = {3x - \dfrac{7}{2}}$ Substitute this expression for $y$ in the first equation. $6x-3({3x - \dfrac{7}{2}}) = 9$ $6x - 9x + \dfrac{21}{2} = 9$ Simplify by combining terms, then solve for $x$ $-3x + \dfrac{21}{2} = 9$ $-3x = -\dfrac{3}{2}$ $x = \dfrac{1}{2}$ Substitute $\dfrac{1}{2}$ for $x$ back into the top equation. $6( \dfrac{1}{2})-3y = 9$ $3-3y = 9$ $-3y = 6$ $y = -2$ The solution is $\enspace x = \dfrac{1}{2}, \enspace y = -2$.